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# 8.1 Exploring Exponential Functions

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### 8.1 Exploring Exponential Functions

1. 1. Suppose two mice live in a barn. If the number of mice quadruples every 4 months, how many mice will there be in 2 years?
2. 3. 8.1 Graphing Exponential Functions
3. 4. Exponential Functions <ul><li>y = a ∙ b x </li></ul><ul><li>Where a = , b = </li></ul><ul><li>Used to model __________________ </li></ul><ul><li>and _______________________ </li></ul>
4. 5. Example 1 . Graph y = 2 ∙ 3 x x y
5. 6. <ul><li>Example 2. </li></ul><ul><li>Determine whether each function models exponential growth or exponential decay. Then find the growth or decay factor. </li></ul><ul><li>y = 100(.12) x </li></ul><ul><li>y = 0.2(5) x </li></ul><ul><li>y = 16( ½ ) x </li></ul>
6. 7. Example 3. In 2000, the annual rate of increase in US population was 1.24%. <ul><li>Predict the population in 2015. </li></ul><ul><li>Why might this not be valid? </li></ul><ul><li>Find the growth rate. </li></ul><ul><li>Write a function to model the growth. </li></ul>http://www.census.gov/population/www/popclockus.html
7. 8. The exponential decay graph shows the expected depreciation for a car over four years. Estimate the value of the car after six years. Example 4 .